CHARACTERISTICS OF QUANTUM OPEN SYSTEMS - FREE RANDOM-VARIABLES APPROACH

Random Matrix Theory provides an interesting tool for modelling a numb er of phenomena where noises (fluctuations) play a prominent role. Var ious applications range from the theory of mesoscopic systems in nucle ar and atomic physics to biophysical models, like Hopfield-type models of neural networks and protein folding. Random Matrix Theory is also used to study dissipative systems with broken time-reversal invariance providing a setup for analysis of dynamic processes in condensed, dis ordered media. In the paper we use the Random Matrix Theory (RMT) with in the formalism of Free Random Variables (alias Blue's functions), wh ich allows to characterize spectral properties of non-Hermitean ''Hami ltonians''. The relevance of using the Blue's function method is discu ssed in connection with application of non-Hermitean operators in vari ous problems of physical chemistry.